Spatial organization in 2D images

A fuzzy definition of the spatial relation “surround” - Application to complex shapes

“…The surround relations proposed in [6,7] are in agreement with the relation we want to define. These definitions allow assessing the degree to which the relation is satisfied between two objects (i.e.…”

“…Another definition of "surround" was proposed in [7]. To evaluate the degree to which an object A is surrounded by B the maximum angle ϕ between two tangent lines of B passing through a point of A is computed (this angle is the same as the one illustrated in green in Figure 1(b)).…”

“…Then the degree to which a region B surrounds a region A is obtained by the center of gravity of the compatibility distribution of the angle histogram H B (A) [7] between A and B and µ surrounds (ϕ). This definition is also in agreement with the definition of surroundedness.…”

Spatial Relations Analysis by Using Fuzzy Operators

“…In relative frame of reference position of a simple object is made with respect to an oriented line or an ordered set forming a vector to some intrinsic properties of reference object. Methods like angle histogram introduced by K.Miyajima and A.Ralescu [1] and statistical method developed by MinDeng.Zalimli [7], R − histogram [8] depends upon relative reference frame. Matsakis [2] introduced 1D representation of 2d objects by the union of longitudinal sections which is the extension of angle histogram.…”

“…Spatial relations play important role in computer vision, scene analysis, geographic information systems (GIS) and content based image retrieval. Analyzing spatial relations by Force histogram was introduced by Miyajima et al [1] and largely developed by Matsakis [2] who used a quantitative representation of relative position between 2D objects. Fuzzy Allen relations are used to define the fuzzy topological relations between different objects and to detect object positions in images.…”